

The proof of the first claim is identical to the proof of [1]}, thus omitted here.

If \(q \in {\text{cut}}(p)\)  then by (REF ) there is \(v \in S_pM\)  such that
\(q=\gamma _{p,v}({\tau _{\text{cut}}}(p,v)), \quad {\tau _{\text{cut}}}(p,v)=\hat{{\tau _{\text{cut}}}}(p,v)\le {\tau _{\text{exit}}}(p,v)<\hat{{\tau _{\text{exit}}}}(p,v),\) 
Thus Lemma REF  and Proposition REF  yield the second claim.

